2024

**Speaker:** Ravi Vakil**When:** Tuesday, April 16, 2024 at 4:00 p.m.**Where:** William E. Kirwan Hall Room 3206**Abstract:** The Mathematics of Doodling

Doodling is a creative and fundamentally human activity, resulting in doodles with intricate and often hidden implicit structure. We will treat doodles as an example for how mathematics is done — by starting with some doodles, we will ask ourselves some natural questions and see where they take us. They will lead us to some unexpected places, and to some sophisticated mathematics.

## 2023

**Speaker:** Steven J Miller**When:** Wednesday, March 29, 2023 at 4:30 p.m.**Where:** William E. Kirwan Hall Room 3206**Abstract:** Why I love Monovariants: From Zombies and Conway's Soldiers to Fibonacci Games

A monovariant is a quantity which is either non-increasing or non-decreasing, such as the number of primes up to *x*, but not the number of factors of n. Many challenging problems can be solved by associating the right monovariant to it; unfortunately it is often challenging to find the right quantity to study. After describing classic problems such as the Zombie Apocalypse and Conway's Soldiers we turn to recent applications.

Zeckendorf proved every positive integer can be written as a sum of non-adjacent Fibonacci numbers (1, 2, 3, 5, 8, ...); using mono-variants we can show no decomposition as a sum of Fibonacci numbers has fewer summands, and discuss generalizations to other sequences. These are key ingredients in analyzing a game involving Fibonacci numbers, where we can prove Player 2 has a winning strategy but it is not known what it is. This work only requires elementary mathematics and is joint with many students (I will mention research opportunities, such as the Polymath Jr REU, for students this summer); there is a $500 reward for a constructive proof of Player 2's winning strategy!

2022

**Speaker:** Barry Cipra**When:** Tuesday, April 19, 2022 at 4:30 p.m.**Where:** William E. Kirwan Hall Room 3206**Abstract:** In Praise of Not Paying Attention

The speaker will describe some mathematical puzzles, problems, and games he has dreamt up over the years while letting his mind wander during math lectures and other occasions. If all goes well, the audience will find it a stimulating presentation…

## 2019

**Speaker:** Jonathan Christopher Mattingly (Duke)**When:** Thursday, April 11, 2019 at 4:00 p.m.**Where:** Toll Physics, Lecture Room 1412**Abstract:** Quantifying Gerrymandering: A Mathematician Goes to Court

In October 2017, I found myself testifying for hours in a Federal In October 2017, I found myself testifying for hours in a Federal court. I had not been arrested. Rather---I was attempting to quantify gerrymandering using mathematical analysis. I was intrigued by the surprising results of the 2012 election, wondering if these results were really surprising. It hinged on probing the geopolitical structure of North Carolina using a Markov Chain Monte Carlo algorithm. In this talk, I will describe the mathematical ideas involved in our analysis. The talk will be accessible and, hopefully, interesting to all, including undergraduates. In fact, this project began as a sequence of undergraduate research projects, which undergraduates continue to be involved with to this day.

## 2018

**Speaker:** Jordan Ellenberg (Wisconsin-Madison)**When:** Friday, April 27, 2018 at 3:30 p.m.**Where:** William E. Kirwan Hall Room 3206**Abstract:** One of the most closely watched Supreme Court cases this year is also one of the most mathematical — Gill v. One of the most closely watched Supreme Court cases this year is also one of the most mathematical — Gill v. Whitford, a case about whether the state legislative districts in Wisconsin were drawn to favor Republicans so greatly that the right of Wisconsin Democrats to representation in the legislature was unconstitutionally diminished. The court will also hear a companion case, Benisek v. Lamone, concerning congressional districts in Maryland, which are drawn to favor Democrats.

As a native of Maryland, a current resident of Wisconsin, and a mathematician, I’m naturally following this closely. How can we use mathematics to test whether district boundaries are drawn to favor one party or the other? How much unfairness is too much? And how can people with mathematical, statistical, and computational training participate in the process and help us get to a point where the legal status quo has good mathematical grounding?

## 2017

**Speaker:** Ingrid Daubechies (Duke)**When:** Thursday, April 27 at 4pm**Where:** William E. Kirwan Hall Room 3206**Abstract:** Mathematics for Art Investigation: Mathematical tools for image analysis increasingly play a role in helping art historians and art conservators assess the state of conversation of paintings, and probe into the secrets of their history. the talk will review several case studies, Van Gogh, Gauguin, Van Eyck among others.

Ingrid Daubechies earned her Ph.D. in theoretical physics from Vrije Universiteit Brussel. In addition to seminal advances in time-frequency analysis, she is best known for her breakthroughs in wavelet research and contributions to digital signal processing. Some of the wavelet bases and other computational techniques she developed were incorporated into the JPEG2000 standard for image compression.

Ingrid's career has seen many impressive firsts: the first female full professor of mathematics at Princeton; the first woman the National Academy of Sciences Award in Mathematics in 2000; the first woman president of the International Mathematics Union in 2010; and she is very likely the first and only mathematician to have been granted the title of Baroness by Belgium's King albert II.

Ingrid continues to break new ground in mathematics research, focusing on signal analysis and inverse problems, with applications ranging from fMRI and geophysics to paleontology and fine art painting.

## 2016

** Dr. Tomaso Poggio (MIT) Speaker:****When:** Thursday, April 28 at 4pm**Where:** John S. Toll Physics Building Room 1412**Abstract:** The birth of artificial-intelligence research as an autonomous discipline is generally thought to have been the month long Dartmouth Summer Research Project on Artificial Intelligence in 1956, which convened 10 leading electrical engineers — including MIT’s Marvin Minsky and Claude Shannon — to discuss “how to make machines use language” and “form abstractions and concepts.” A decade later, impressed by rapid advances in the design of digital computers, Minsky was emboldened to declare that “within a generation ... the problem of creating ‘artificial intelligence’ will substantially be solved.”

The problem, of course, turned out to be much more difficult than AI’s pioneers had imagined. In recent years, by exploiting machine learning — in which computers learn to perform tasks from sets of training examples — artificial-intelligence researchers have built special-purpose systems that can do things like interpret spoken language or play professional-level Go games or drive cars using vision. Some of the present excitement is due to realistic expectations for further progress.

There is also a substantial amount of hype. However, systems that are intelligent in narrow domains are being developed.

I will briefly review today’s engineering of intelligence and some of the mathematics underlying it, the mathematics of learning from data. I will also sketch the vision of the MIT Center for Brains, Minds and Machines which strives to make progress on the science of intelligence.

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## 2015

**The Inaugural William E. Kirwan Distinguished Undergraduate Lecture**

**Feuerbach’s Theorem: A Beautiful Theorem Deserves a Beautiful Proof" by Professor Douglas Hofstadter* on April 23rd, 2015 4:00-5:00pm in Physics 1412. **

Douglas Hofstadter is a College of Arts and Sciences Distinguished Professor of Cognitive Science at Indiana University, Director of the Center for Research on Concepts and Cognition, and the author of the Pulitzer Prizewinning book, Gödel, Escher, Bach: an Eternal Golden Braid.

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